1,220 research outputs found
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
Equivalence of robust stabilization and robust performance via feedback
One approach to robust control for linear plants with structured uncertainty
as well as for linear parameter-varying (LPV) plants (where the controller has
on-line access to the varying plant parameters) is through
linear-fractional-transformation (LFT) models. Control issues to be addressed
by controller design in this formalism include robust stability and robust
performance. Here robust performance is defined as the achievement of a uniform
specified -gain tolerance for a disturbance-to-error map combined with
robust stability. By setting the disturbance and error channels equal to zero,
it is clear that any criterion for robust performance also produces a criterion
for robust stability. Counter-intuitively, as a consequence of the so-called
Main Loop Theorem, application of a result on robust stability to a feedback
configuration with an artificial full-block uncertainty operator added in
feedback connection between the error and disturbance signals produces a result
on robust performance. The main result here is that this
performance-to-stabilization reduction principle must be handled with care for
the case of dynamic feedback compensation: casual application of this principle
leads to the solution of a physically uninteresting problem, where the
controller is assumed to have access to the states in the artificially-added
feedback loop. Application of the principle using a known more refined
dynamic-control robust stability criterion, where the user is allowed to
specify controller partial-state dimensions, leads to correct
robust-performance results. These latter results involve rank conditions in
addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page
H∞ control of nonlinear systems: a convex characterization
The nonlinear H∞-control problem is considered with an emphasis on developing machinery with promising computational properties. The solutions to H∞-control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems. The computational implications for the characterization are discussed
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